void
dft_PolyA11_Tpetra_Operator<Scalar,MatrixType>::
Check
(bool verbose) const
{
RCP<VEC > x = rcp(new VEC(getDomainMap()));
RCP<VEC > b = rcp(new VEC(getRangeMap()));
x->randomize(); // Fill x with random numbers
apply(*x, *b); // Forward operation
applyInverse(*b, *b); // Reverse operation
b->update(-STS::one(), *x, STS::one()); // Should be zero
Scalar absResid = b->norm2();
Scalar normX = x->norm2();
Scalar resid = absResid / normX;
if (verbose)
{
std::cout << "A11 self-check residual = " << resid << std::endl;
}
TEUCHOS_TEST_FOR_EXCEPTION(resid > 1.0E-12, std::runtime_error, "Bad residual.\n");
} //end Check
void
dft_PolyA22_Tpetra_Operator<Scalar,MatrixType>::
Check
(bool verbose) const
{
RCP<VEC > x = rcp(new VEC(getDomainMap()));
RCP<VEC > b = rcp(new VEC(getRangeMap()));
x->randomize(); // Fill x with random numbers
apply(*x, *b); // Forward operation
if (hasDensityOnCms_)
{
if (F_location_ == 1) //F in NE
{
// Inverse is not exact, so we must modify b2 first:
RCP<MV> x1 = x->offsetViewNonConst(cmsMap_, 0);
// Start x1 to view first numCmsElements elements of x
RCP<MV> b2 = b->offsetViewNonConst(densityMap_, cmsMap_->getNodeNumElements());
// Start b2 to view last numDensity elements of b
RCP<MV > DCx1 = rcp(new MV(*b2));
densityOnCmsMatrixOp_->apply(*x1, *DCx1);
b2->update(-STS::one(), *DCx1, STS::one()); // b2 = b2 - DC*x1
}
else
{
// Inverse is not exact, so we must modify b1 first:
RCP<MV> x2 = x->offsetViewNonConst(cmsMap_, densityMap_->getNodeNumElements());
//Start x2 to view last numCms elements of x
RCP<MV> b1 = b->offsetViewNonConst(densityMap_, 0);
// Start b1 to view first numDensity elements of b
RCP<MV > DCx2 = rcp(new MV(*b1));
densityOnCmsMatrixOp_->apply(*x2, *DCx2);
b1->update(-STS::one(), *DCx2, STS::one()); // b1 = b1 - DC*x2
}
}
// Reverse operation
applyInverse(*b, *b);
b->update(-STS::one(), *x, STS::one()); // Should be zero
Scalar resid = b->norm2();
if (verbose)
{
std::cout << "A22 self-check residual = " << resid << std::endl;
}
TEUCHOS_TEST_FOR_EXCEPTION(resid > 1.0E-12, std::runtime_error, "Bad residual.\n");
} //end Check
int invIteration(Epetra_CrsMatrix& A, double &lambda, bool verbose) {
Ifpack_CrsRiluk * M;
applyInverseSetup(A, M);
Epetra_Vector q(A.RowMap());
Epetra_Vector z(A.RowMap());
Epetra_Vector resid(A.RowMap());
Epetra_Flops * counter = A.GetFlopCounter();
if (counter!=0) {
q.SetFlopCounter(A);
z.SetFlopCounter(A);
resid.SetFlopCounter(A);
}
// Fill z with random Numbers
z.Random();
// variable needed for iteration
double normz, residual;
int niters = 100;
double tolerance = 1.0E-6;
int ierr = 1;
for (int iter = 0; iter < niters; iter++)
{
if (verbose)
cout << endl
<< " ***** Performing step " << iter << " of inverse iteration ***** " << endl;
z.Norm2(&normz); // Compute 2-norm of z
q.Scale(1.0/normz, z);
applyInverse(A, z, q, M, verbose); // Compute z such that Az = q
q.Dot(z, &lambda); // Approximate maximum eigenvalue
if (iter%10==0 || iter+1==niters)
{
resid.Update(1.0, z, -lambda, q, 0.0); // Compute A(inv)*q - lambda*q
resid.Norm2(&residual);
cout << endl
<< "***** Inverse Iteration Step " << iter+1 << endl
<< " Lambda = " << 1.0/lambda << endl
<< " Residual of A(inv)*q - lambda*q = "
<< residual << endl;
}
if (residual < tolerance) {
ierr = 0;
break;
}
}
// lambda is the largest eigenvalue of A(inv). 1/lambda is smallest eigenvalue of A.
lambda = 1.0/lambda;
// Compute A*q - lambda*q explicitly
A.Multiply(false, q, z);
resid.Update(1.0, z, -lambda, q, 0.0); // Compute A*q - lambda*q
resid.Norm2(&residual);
cout << " Explicitly computed residual of A*q - lambda*q = " << residual << endl;
applyInverseDestroy(M);
return(ierr);
}
